An Explanation of Sail Flow Analysis

Introduction

Stanford Yacht Research (SYR) is currently doing a study in performance analysis on yacht sails through experimental and computational methods. This research is being done to study the flow around sails in a wind tunnel and to validate computer results against experimental results.

Those involved with the present research include:

Dr. Margot Gerritsen, Stanford Yacht Research

Dr. Andrew Crook, NASA Ames Research Center

Tyler Doyle, Ph.D. student at Stanford University

Sriram Shankaran, Ph.D. student at Stanford University

Steve Collie, Ph.D. student at University of Auckland

Jean-Edmond Coutris, Graduate student at Stanford University

Brendan Abbott, SYR intern - undergraduate at Webb Institute

Daniela Hanson, SYR intern - undergraduate at Webb Institute

Center for Turbulence Research (CTR)

Aero-Astro Department

NASA Ames Research Center

Sail Design

Working toward designing more and more efficient sails throughout history, many methods have been employed. From the beginning of sail design, intuition and experience have been the primary means of designing sails. Intuition and experience still play a major role in sail design because presently no database exists to tell a sailboat designer what sail will work best with a given hull shape!

From intuition, prototype sails can be built to test a design and measure its effectiveness. Also, wind tunnel testing can be done with model sails to observe and study the flow around sails on a smaller scale.

Today, computers have become a means of calculating a lot of information in short amounts of time. Computer programs that employ the Navier-Stokes fluid mechanics equations can provide answers to very complicated and long flow equations in relatively short amounts of time. Through experimental testing, flow results calculated by computers can be validated. In the near future, it is possible that computers will be able to fully simulate flow on a sail. Today, the power and speed of computers limits what work can be done to analyze flow.

How Does Air Flow Past a Sail

BASIC FUNCTION OF SAILS

Sails are instruments that use the wind to propel a vessel through the water. Trimming the sails differently allows a vessel to sail at different angles to the wind.

AIR FLOW AT DIFFERENT SAIL ANGLES

Upwind Sailing - In upwind sailing, sails act similarly to foils. The forces generated by the sail result in lifting forces generated by the keel, and forward motion is produced. (A FURTHER EXPLANATION OF THE BASIC PHYSICS OF UPWIND SAILING CAN BE FOUND IN THE PHYSICS OF SAILING )

Reaching

Downwind Sailing - Sails are used to catch the wind. The wind is used to "push" the boat along.

Twist

To describe how air flows past a sail, we must describe how air flows over the water. To simplify things, let's first assume that the water is not moving. At the water's surface, the air is moving at the same speed as the water. Thus, the air cannot be moving at the water's surface.

However, if there is wind, we know that the air must be moving as we move away from the water. Because the true wind speed is greater further up the mast, the apparent wind created by the boat's forward velocity causes a "twisting" phenomenon:

Upwind Twist Diagram

The effect of twist is more apparent in downwind sailing. An International AmericaÍs Cup Class (IACC) yacht, because of its ability to sail downwind close to the speed of the wind, never really sails downwind at all. The IACC yachts are always experiencing apparent wind angles that simulate reaching conditions (about 90 degrees), rather than downwind conditions.

Downwind Twist Diagram

Difficulty of Modeling Actual 3D Sails

Modeling of sails is difficult because the conditions that a sail experiences fluctuate tremendously. Trim, wind speed, boat speed, heel angle, and weather all change over time. These factors change the way a sail will perform. Also, flow patterns due to twist are hard to model in 3-D computer applications because of the complexity of eddies shedding from the head and foot of the sail.

In This Study, SYR is Using 2D Sections

Rather than modeling 3-D sections, a 2-D section of a sail is used to reduce computational cost. 2-D sections are representative of flow at a given height on the sail.

The 2-D sections are optimized with computer programs. The flow patterns generated from a 2-D section, although simplified, are not completely irrelevant. Sail-makers still use optimized 2-D sections to create a 3-D sail. Generally, ten to twenty 2-D sections are used in making a sail.

Computational Fluid Dynamics

The computer application that SYR uses to analyze flow is a Computational Fluid Dynamics (CFD) program. CFD is a method that employs fluid mechanics equations to describe flow.

A shape, such as a sail section, is created in the CFD program. It is the computer's task to calculate the flow field around the shape. However, there are an infinite amount of points around the shape. Calculating the flow in an undefined region would take decades. Therefore, a grid must be created around the shape to break down the computational process into a finite number of calculations. The grid is a crucial part of the solution process. If it is not dense enough, the flow solution will be lacking. If the grid is too dense, calculations will be too computationally expensive. This is the challenge of producing good CFD results.

After a satisfactory grid is created, the CFD program can run. A flow analysis on a 2-D section takes about 5 hours to run on a high quality computer (such as a Pentium 4). The results obtained from CFD are velocities at all grid points, pressure distributions, and forces acting on the sail section. Forces acting on the sail are determined by integrating the pressure distribution over the sail area.

Velocities at All Grid Points

Pressure Distribution and Streamlines

Forces Derived from Pressure Distribution

Wind Tunnel Testing

To validate the CFD results, 2-D sections are also being tested by SYR in the 7 ft x 10 ft wind tunnel at NASA Ames. To create a 2-D model for the wind tunnel, a "slice" of a sail is taken. This slice is scaled down to a chord length of 2/3 of a foot; then, it is stretched to a height of 10 feet.

The model is created with a high aspect ratio to try to eliminate vertical flow. A real sail has a flow pattern like this:

We only want to analyze the sail flow in two dimensions:

The basic wind tunnel setup looks like this:

Model Construction

Data Acquisition in the Wind Tunnel

What Does This Tell Us About Sailing?

The use of CFD and wind tunnel testing gives insight into flow around sails and improves CFD codes. Better understanding of flow around sails will hopefully produce more efficiently designed sails in the future.

Results from sail modeling tell us, for example, about the importance of trim, staying in "clean air", and how the main and foresail interact.

Importance of Trim: If the sail is not trimmed correctly, it is not efficient. Over-trimming causes excessive turbulence on the leeward side of the sail. Under-trimming greatly reduces the forces produced by the sail. Ideal trim produces the best flow distribution around the sail.

Effect of Upwind Boat and "Dirty" Air: The downwind boat cannot point as high as the upwind boat because of the effect of the flow around the sails of the upwind boat.

Main and foresail interaction: The flow around the mainsail speeds up the air at the trailing edge of the foresail, making it more efficient. The air flowing past the mainsail helps the jib sail at a smaller angle of attack.

Limitations of Modern Sail Research

In computer and wind tunnel simulations, simplifications are made to the sail's environment. First of all, the sail is analyzed independently of hull and water. A rigid sail is used in an upright position. To completely model a real sail it would be necessary to use a flexible 3-dimensional sail in a heeled position, and to consider the effects of the hull and sea state. However, modeling something like this would be far too computationally expensive.

In the future, with a growing amount of power and speed in the computer, the possibility of analyzing more complicated systems will be greater.